wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In a trapezium PQRS, as shown in the figure, PQ || SR || TU . If TP=12PS, then the ar(PQRS) is equal to


A

4[ar(STUR)ar(ΔVSR)]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

2ar(PQUT)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

2ar(ΔSRQ)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

2ar(ΔQPS)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A
4[ar(STUR)ar(ΔVSR)]
Given that PQRS is a trapezium such that TP=12 PS and PQ||SR||TU.

In ΔSPN, by the converse of mid-point theorem,

SO=ON (TO||PN)

Consider: 4[Ar(STUR)Ar(ΔVSR)]=4[(12×(TU+RS)×SN2)(12×RS×SN2)]=4(12×TU×SN2)=TU×SN

Now, T is the mid-point of SP.

In ΔSPQ, by the converse of mid-point theorem,

SV=VQ (TV||PQ) Thus, V is the mid-point of SQ,Similarly, in ΔSRQ, by the converse of mid-point theorem, RU=UQ (VU||SR)

Thus, U is the mid-point of RQ.

Also, TV=12 PQ and VU=12SRTV+VU=12×(PQ+SR)TU=12×(PQ+SR)...(ii)4[Ar(STUR)Ar(Δ VSR)]=TU×SN [From (i)]=12×(PQ+SR)×SN [From (i) and (ii) ]=Ar(PQRS)

Hence, the correct answer is option (a).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon